Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Towards Practical Mean Bounds for Small Samples
Authors: My Phan, Philip Thomas, Erik Learned-Miller
ICML 2021 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In simulations, we show that for many distributions, the gain over Anderson s bound is substantial. 5. Simulations We perform simulations to compare our bounds to Hoeffding s inequality, Anderson s bound, Maurer and Pontil s, and Student-t s bound (Student, 1908), the latter being |
| Researcher Affiliation | Academia | My Phan 1 Philip S. Thomas 1 Erik Learned-Miller 1 1College of Information and Computer Sciences, University of Massachusetts, Amherst, MA, USA. Correspondence to: My Phan <EMAIL>. |
| Pseudocode | Yes | Algorithm 1 Monte Carlo estimation of mĪ± D+,T (x) where D+ = [0, 1]. This pseudocode uses 1-based array indexing. |
| Open Source Code | Yes | Code accompanying this paper is available at https://github.com/myphan9/small_sample_mean_bounds. |
| Open Datasets | No | We perform experiments on three distributions: beta(1, 5) (skewed right), uniform(0, 1) and beta(5, 1) (skewed left). Their PDFs are included in the supplementary material for reference. The paper uses synthetic data generated from these distributions, not pre-existing publicly available datasets that require a specific link or citation for access. |
| Dataset Splits | No | The paper conducts simulations by sampling from specified distributions (beta(1,5), uniform(0,1), beta(5,1)) for various sample sizes, but does not mention traditional train/validation/test dataset splits as it's not training a model on a fixed dataset. |
| Hardware Specification | No | The paper does not provide specific details about the hardware (e.g., CPU, GPU models, or memory specifications) used for running the simulations. |
| Software Dependencies | No | The paper describes algorithms and statistical methods, but does not specify any software dependencies or libraries with version numbers (e.g., Python, PyTorch, SciPy versions) used for implementation or simulation. |
| Experiment Setup | Yes | We use Ī± = 0.05, D+ = [0, 1] and l = 10,000 Monte Carlo samples. We consider two functions T: 1. Anderson: T(x) = bĪ±,Anderson ā (x), again with ā= u And. Because this T is linear in x, it can be computed with the linear program in Eq. 42. 2. l2 norm: T(x) = (Pn i=1 x2 i )/n. |